Demographics | Physical health | Hearing | Cognition | Mobility and balance | Quality of life | Mental health | Social participation and support | Views on hearing loss |
Logistic regression and other statistical methods require complete cases. In our case, with 40+ variables of interest, dropping participants with any missing values leads to a sample size of 200+ cases instead of 500+. There is loss of power, and estimates from models will likely be biased. The goal of missing data imputation is to restore variance of the sample to make it better reflect characteristics of the population (i.e., give accurate estimates of standard errors, CI’s, and p-values).
Say there are three variables ‘A’, ‘B’, and ‘C’, each with some missing values. Choose variable ‘A’ to start filling in. Fill in missing values in ‘B’ and ‘C’ with temporary values, such as the mean.
Predict missing ‘A’, using A ~ B + C, adding a random component. Move on to predicting missing ‘B’, using B ~ A + C and including predicted ‘A’, again adding a random component. Move on to predicting missing ‘C’, using C ~ A + B and predicted ‘B’. This is one cycle.
Choose the number of cycles, say 10 iterations. At the end of 10 iterations, an “imputed” dataset is formed with complete cases. Choose the number of imputed datasets to form (the same analysis will be conducted on each slightly different dataset, and the results will be pooled). Choose which variables should be used as predictors of other variables. Choose which method to use for predicting missing values, e.g., predictive mean matching. For derived variables such as summed scores, consider whether to impute components first and then calculate derived scores, or impute derived scores. Consider whether there should be an order of which variables to start imputing first.
Check whether the imputed data “converge” (the means and SEs stabilize after a few iterations, and are similar across imputed datasets). Check the distributions and characteristics of imputed data (e.g. integer-only values, floors and ceilings, plausibility), and their similarity to observed data.
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## 0 | 00004444444444444444444444444444444444444999999999999999999999999999+193
## 2 | 22222222222222222222222222222222222222222277777777777777777777777777+16
## 4 | 000044444999993333333888888888888
## 6 | 222222222222222666666666666666666111111111111111111155555555555
## 8 | 0000000004444888833337777
## 10 | 221199
## 12 | 488
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## 98 | 66
Participants with <26% missing data (n=509):
Participants with >42% missing data (n=18):
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## 0 | 00000000000000000000000000000000000000000000000000000000000000000000+152
## 2 | 33333333333333333333333333333333333333333333333333333333333333333333+50
## 4 | 555555555555555555555555555555555555555555555
## 6 | 88888888888888888888888888888888888888888888888888888888888
## 8 | 1111111111111111111111111
## 10 | 444444444444
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## 90 | 99
Participants with <20% missing data (n=509):
## # A tibble: 44 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 0 0
## 2 Age 2 0.393
## 3 Retired_bin 0 0
## 4 Volunteer 0 0
## 5 Lives_alone_bin 0 0
## 6 Phys_health_rating 7 1.38
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 18 3.54
## 9 Subj_vision_rating_aided 1 0.196
## 10 Subj_hearing_loss_bin 36 7.07
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided 159 31.2
## 14 Subj_hearing_rating_unaided 8 1.57
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech 46 9.04
## 17 ssq_spatial 51 10.0
## 18 ssq_qualities 3 0.589
## 19 SIM_mean 12 2.36
## 20 Emocheq_mean 8 1.57
## 21 hhies_emo_total 0 0
## 22 hhies_soc_total 0 0
## 23 positive_SCI_bin 0 0
## 24 CSRQ_mean 0 0
## 25 Mobility_needs_bin 0 0
## 26 ABC_mean 0 0
## 27 SWLS_mean 0 0
## 28 WHOQOL_overall_qol 0 0
## 29 WHOQOL_health_qol 0 0
## 30 WHOQOL_Dom1_phys 0 0
## 31 WHOQOL_Dom2_psy 0 0
## 32 WHOQOL_Dom3_soc 1 0.196
## 33 WHOQOL_Dom4_env 0 0
## 34 WHO_money 0 0
## 35 PHQ4_mean 1 0.196
## 36 Lonely_bin 1 0.196
## 37 Social_network_index 1 0.196
## 38 Soc_part_freq 1 0.196
## 39 Soc_part_types 1 0.196
## 40 Connections_total 9 1.77
## 41 Motivate_mean 5 0.982
## 42 HA.Purchase 78 15.3
## 43 PTA4_better_ear 73 14.3
## 44 PTA4_asym 74 14.5
Participants with >39%% missing data (n=18):
## # A tibble: 43 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 2 11.1
## 2 Age 3 16.7
## 3 Retired_bin 2 11.1
## 4 Volunteer 2 11.1
## 5 Lives_alone_bin 2 11.1
## 6 Phys_health_rating 4 22.2
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 4 22.2
## 9 Subj_vision_rating_aided 4 22.2
## 10 Subj_hearing_loss_bin 5 27.8
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided 10 55.6
## 14 Subj_hearing_rating_unaided 5 27.8
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech 15 83.3
## 17 ssq_spatial 13 72.2
## 18 ssq_qualities 8 44.4
## 19 SIM_mean 13 72.2
## 20 Emocheq_mean 13 72.2
## 21 hhies_emo_total 15 83.3
## 22 hhies_soc_total 15 83.3
## 23 positive_SCI_bin 15 83.3
## 24 CSRQ_mean 17 94.4
## 25 Mobility_needs_bin 17 94.4
## 26 ABC_mean 17 94.4
## 27 SWLS_mean 17 94.4
## 28 WHOQOL_overall_qol 18 100
## 29 WHOQOL_health_qol 18 100
## 30 WHOQOL_Dom1_phys 18 100
## 31 WHOQOL_Dom2_psy 18 100
## 32 WHOQOL_Dom3_soc 18 100
## 33 WHOQOL_Dom4_env 18 100
## 34 WHO_money 18 100
## 35 PHQ4_mean 18 100
## 36 Lonely_bin 18 100
## 37 Social_network_index 18 100
## 38 Soc_part_freq 18 100
## 39 Soc_part_types 18 100
## 40 Connections_total 18 100
## 41 Motivate_mean 18 100
## 42 HA.Purchase 5 27.8
## 43 PTA4_better_ear 5 27.8
Complete cases out of n=527 (none of 44 variables missing):
## [1] 232
## [1] 44.02277
## # A tibble: 44 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 2 100
## 2 Age 2 100
## 3 Retired_bin 2 100
## 4 Volunteer 2 100
## 5 Lives_alone_bin 2 100
## 6 Phys_health_rating 2 100
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 2 100
## 9 Subj_vision_rating_aided 2 100
## 10 Subj_hearing_loss_bin 2 100
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided 2 100
## 14 Subj_hearing_rating_unaided 2 100
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech 2 100
## 17 ssq_spatial 2 100
## 18 ssq_qualities 2 100
## 19 SIM_mean 2 100
## 20 Emocheq_mean 2 100
## 21 hhies_emo_total 2 100
## 22 hhies_soc_total 2 100
## 23 positive_SCI_bin 2 100
## 24 CSRQ_mean 2 100
## 25 Mobility_needs_bin 2 100
## 26 ABC_mean 2 100
## 27 SWLS_mean 2 100
## 28 WHOQOL_overall_qol 2 100
## 29 WHOQOL_health_qol 2 100
## 30 WHOQOL_Dom1_phys 2 100
## 31 WHOQOL_Dom2_psy 2 100
## 32 WHOQOL_Dom3_soc 2 100
## 33 WHOQOL_Dom4_env 2 100
## 34 WHO_money 2 100
## 35 PHQ4_mean 2 100
## 36 Lonely_bin 2 100
## 37 Social_network_index 2 100
## 38 Soc_part_freq 2 100
## 39 Soc_part_types 2 100
## 40 Connections_total 2 100
## 41 Motivate_mean 2 100
## 42 HA.Purchase 2 100
## 43 PTA4_better_ear 2 100
## 44 PTA4_asym 2 100
## # A tibble: 44 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Gender_bin 0 0
## 2 Age 1 6.25
## 3 Retired_bin 0 0
## 4 Volunteer 0 0
## 5 Lives_alone_bin 0 0
## 6 Phys_health_rating 2 12.5
## 7 Multimorbidity_score 0 0
## 8 Subj_vision_loss_bin 2 12.5
## 9 Subj_vision_rating_aided 2 12.5
## 10 Subj_hearing_loss_bin 3 18.8
## 11 any_hearing_device 0 0
## 12 study2_HA 0 0
## 13 Subj_hearing_rating_aided 8 50
## 14 Subj_hearing_rating_unaided 3 18.8
## 15 Tinnitus_past_wk_bin 0 0
## 16 ssq_speech 13 81.2
## 17 ssq_spatial 11 68.8
## 18 ssq_qualities 6 37.5
## 19 SIM_mean 11 68.8
## 20 Emocheq_mean 11 68.8
## 21 hhies_emo_total 13 81.2
## 22 hhies_soc_total 13 81.2
## 23 positive_SCI_bin 13 81.2
## 24 CSRQ_mean 15 93.8
## 25 Mobility_needs_bin 15 93.8
## 26 ABC_mean 15 93.8
## 27 SWLS_mean 15 93.8
## 28 WHOQOL_overall_qol 16 100
## 29 WHOQOL_health_qol 16 100
## 30 WHOQOL_Dom1_phys 16 100
## 31 WHOQOL_Dom2_psy 16 100
## 32 WHOQOL_Dom3_soc 16 100
## 33 WHOQOL_Dom4_env 16 100
## 34 WHO_money 16 100
## 35 PHQ4_mean 16 100
## 36 Lonely_bin 16 100
## 37 Social_network_index 16 100
## 38 Soc_part_freq 16 100
## 39 Soc_part_types 16 100
## 40 Connections_total 16 100
## 41 Motivate_mean 16 100
## 42 HA.Purchase 3 18.8
## 43 PTA4_better_ear 3 18.8
## 44 PTA4_asym 3 18.8
Current method:
* predictors that correlate 0.5 or better (30 variables); if no such
predictors, adjust threshold to 0.4 (3 variables), then 0.3, then 0.2 (2
variables)
* total of 5 imputed datasets, with a maximum of 10 iterations per
dataset
Note: Not filtered by hearing aid candidacy according to threshold(s) at 2kHz.
Non-hearing aid users = 166
Hearing aid users = 80 (31%)
Significant predictors:
- Subj_hearing_rating_aided
- Subj_hearing_rating_unaided
- SWLS_mean
- PTA4_better_ear
“Borderline”: SSQ15i_mean, SWLS_mean
##
## Call:
## glm(formula = formula_adopt, family = "binomial", data = compdata_ad)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.27e+01 1.45e+03 -0.02 0.982
## Gender_bin 1.60e+00 1.04e+00 1.53 0.125
## Age -6.49e-02 6.30e-02 -1.03 0.303
## Retired_bin 2.67e-01 1.06e+00 0.25 0.802
## Volunteer_rec 8.99e-01 5.39e-01 1.67 0.095 .
## Lives_alone_bin -1.20e+00 1.15e+00 -1.04 0.297
## Phys_health_rating 3.96e-01 7.82e-01 0.51 0.613
## Multimorbidity_score 2.83e-01 2.47e-01 1.14 0.252
## Subj_vision_rating_aided -6.52e-01 6.09e-01 -1.07 0.284
## Subj_hearing_loss_bin 1.90e+01 1.45e+03 0.01 0.990
## Subj_hearing_rating_aided 4.41e+00 9.34e-01 4.72 2.4e-06 ***
## Subj_hearing_rating_unaided -3.68e+00 9.40e-01 -3.92 9.0e-05 ***
## Tinnitus_past_wk_bin -4.05e-01 7.64e-01 -0.53 0.596
## SSQ15i_mean 6.87e-01 3.75e-01 1.83 0.067 .
## SIM_mean 1.31e-01 2.69e-01 0.49 0.626
## Emocheq_mean -4.70e-01 6.02e-01 -0.78 0.435
## HHIES_total -7.49e-03 7.64e-02 -0.10 0.922
## positive_SCI_bin 3.05e-03 1.28e+00 0.00 0.998
## CSRQ_mean 5.96e-01 1.23e+00 0.48 0.628
## Mobility_needs_bin -8.07e-01 2.07e+00 -0.39 0.696
## ABC_mean -4.59e-02 5.63e-02 -0.82 0.415
## SWLS_mean 1.26e+00 6.66e-01 1.90 0.058 .
## WHOQOL_overall_qol -8.50e-01 8.79e-01 -0.97 0.334
## WHOQOL_health_qol 3.34e-02 6.71e-01 0.05 0.960
## WHO_money 9.77e-01 6.28e-01 1.56 0.120
## PHQ4_mean 8.12e-01 1.02e+00 0.80 0.424
## Lonely_bin 2.35e+00 1.59e+00 1.48 0.140
## Social_network_index -2.77e-01 4.01e-01 -0.69 0.490
## Soc_part_freq 4.03e-01 6.62e-01 0.61 0.542
## Soc_part_types 1.14e-01 4.12e-01 0.28 0.782
## Motivate_mean -8.83e-01 6.04e-01 -1.46 0.144
## PTA4_better_ear 1.64e-01 6.19e-02 2.65 0.008 **
## PTA4_asym 6.53e-02 4.40e-02 1.48 0.138
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 310.319 on 245 degrees of freedom
## Residual deviance: 70.645 on 213 degrees of freedom
## AIC: 136.6
##
## Number of Fisher Scoring iterations: 19
Significant predictors:
- Volunteering
- Subj_hearing_rating_aided
- Subj_hearing_rating_unaided
- SSQ15i_mean
- ABC_mean (balance)
- PHQ4_mean (anxiety & depression)
- PTA4_better_ear
“Borderline”: Subj_hearing_loss_bin, SWLS_mean, PTA4_asym
## term estimate std.error statistic df
## 1 (Intercept) -0.806931 0.34769 -2.3208 222.0
## 2 Gender_bin 0.021310 0.03559 0.5988 181.1
## 3 Age 0.003095 0.00246 1.2588 147.7
## 4 Retired_bin -0.032932 0.03481 -0.9460 374.0
## 5 Volunteer_rec 0.038470 0.02101 1.8306 103.0
## 6 Lives_alone_bin -0.042122 0.04062 -1.0370 108.1
## 7 Phys_health_rating 0.004897 0.02482 0.1973 479.6
## 8 Multimorbidity_score 0.001020 0.00750 0.1361 221.4
## 9 Subj_vision_rating_aided -0.001435 0.02207 -0.0650 364.4
## 10 Subj_hearing_loss_bin 0.084453 0.05560 1.5189 32.8
## 11 Subj_hearing_rating_aided 0.168911 0.02645 6.3857 14.7
## 12 Subj_hearing_rating_unaided -0.185798 0.02806 -6.6221 95.8
## 13 Tinnitus_past_wk_bin -0.023344 0.03424 -0.6817 195.9
## 14 SSQ15i_mean 0.034027 0.01415 2.4052 113.4
## 15 SIM_mean -0.000315 0.00751 -0.0419 455.6
## 16 Emocheq_mean -0.003042 0.01989 -0.1530 406.6
## 17 HHIES_total 0.003377 0.00273 1.2349 346.7
## 18 positive_SCI_bin 0.044843 0.05332 0.8410 352.3
## 19 CSRQ_mean -0.017025 0.04653 -0.3659 346.0
## 20 Mobility_needs_bin -0.038533 0.08087 -0.4765 212.8
## 21 ABC_mean -0.002613 0.00169 -1.5481 76.6
## 22 SWLS_mean 0.028278 0.01900 1.4884 125.9
## 23 WHOQOL_overall_qol 0.002644 0.03723 0.0710 53.5
## 24 WHOQOL_health_qol 0.023161 0.02321 0.9977 102.0
## 25 WHO_money 0.020299 0.02171 0.9349 31.7
## 26 PHQ4_mean 0.105739 0.03916 2.7000 323.4
## 27 Lonely_bin -0.022285 0.04441 -0.5018 264.7
## 28 Social_network_index -0.004301 0.01363 -0.3155 170.1
## 29 Soc_part_freq 0.011107 0.02588 0.4292 348.6
## 30 Soc_part_types -0.005587 0.01203 -0.4646 306.5
## 31 Motivate_mean 0.013979 0.01824 0.7665 417.4
## 32 PTA4_better_ear 0.006290 0.00236 2.6686 30.8
## 33 PTA4_asym 0.002822 0.00137 2.0568 268.7
## p.value
## 1 0.02120233522
## 2 0.55005795287
## 3 0.21009235277
## 4 0.34473620735
## 5 0.07004677534
## 6 0.30207256120
## 7 0.84367579472
## 8 0.89189094520
## 9 0.94817121264
## 10 0.13835503875
## 11 0.00001364278
## 12 0.00000000205
## 13 0.49622080463
## 14 0.01778290761
## 15 0.96656950876
## 16 0.87848051123
## 17 0.21772209100
## 18 0.40094044650
## 19 0.71466602722
## 20 0.63423152530
## 21 0.12572603219
## 22 0.13914887054
## 23 0.94365542571
## 24 0.32078585807
## 25 0.35688509994
## 26 0.00729834245
## 27 0.61623759233
## 28 0.75273205234
## 29 0.66806390936
## 30 0.64255848258
## 31 0.44381423125
## 32 0.01204445210
## 33 0.04066669579
Significant predictors:
- Lives_alone
- Phys_health_rating
- Subj_hearing_rating_unaided
- HHIES_total
- Social_network_index
“Borderline”: Gender, Multimorbidity, Tinnitus_past_wk_bin, WHOQOL_health_qol
##
## Call:
## glm(formula = formula_subj, family = "binomial", data = compdata_subj)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.2020 11.3264 0.64 0.52487
## Gender_bin 2.3178 1.2441 1.86 0.06245 .
## Age 0.0976 0.0739 1.32 0.18666
## Retired_bin 0.5018 1.0368 0.48 0.62839
## Volunteer_rec -0.2510 0.5229 -0.48 0.63126
## Lives_alone_bin 3.5598 1.4045 2.53 0.01126 *
## Phys_health_rating 2.4966 1.0660 2.34 0.01918 *
## Multimorbidity_score 0.4884 0.2646 1.85 0.06492 .
## Subj_vision_rating_aided 0.7719 0.6506 1.19 0.23547
## Subj_hearing_rating_aided 1.2644 0.8375 1.51 0.13113
## Subj_hearing_rating_unaided -4.8025 1.2674 -3.79 0.00015 ***
## Tinnitus_past_wk_bin 1.7299 0.9840 1.76 0.07875 .
## SSQ15i_mean 0.0856 0.6418 0.13 0.89389
## SIM_mean -0.1458 0.2962 -0.49 0.62261
## Emocheq_mean -0.7131 0.7718 -0.92 0.35549
## HHIES_total 0.3582 0.1319 2.72 0.00661 **
## positive_SCI_bin 0.7450 1.4751 0.51 0.61353
## CSRQ_mean -1.2015 1.2809 -0.94 0.34824
## Mobility_needs_bin 3.7661 3.1341 1.20 0.22951
## ABC_mean -0.0398 0.0953 -0.42 0.67607
## SWLS_mean -0.2584 0.5202 -0.50 0.61940
## WHOQOL_overall_qol -0.8334 0.9269 -0.90 0.36858
## WHOQOL_health_qol -1.8178 0.9457 -1.92 0.05457 .
## WHO_money 0.5510 0.5579 0.99 0.32332
## PHQ4_mean -1.2715 1.4615 -0.87 0.38429
## Lonely_bin -2.7214 1.6810 -1.62 0.10546
## Social_network_index 0.8271 0.3570 2.32 0.02052 *
## Soc_part_freq -0.9624 0.8004 -1.20 0.22919
## Soc_part_types -0.6853 0.4417 -1.55 0.12079
## Motivate_mean -0.5373 0.6708 -0.80 0.42316
## PTA4_better_ear 0.1047 0.0706 1.48 0.13819
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 317.160 on 245 degrees of freedom
## Residual deviance: 59.256 on 215 degrees of freedom
## AIC: 121.3
##
## Number of Fisher Scoring iterations: 9
Significant predictors:
- Subj_vision_rating_aided
- Subj_hearing_rating_unaided
- Tinnitus_past_wk_bin
- HHIES_total
- PTA4_better_ear
“Borderline”: Emocheq_mean
## term estimate std.error statistic df p.value
## 1 (Intercept) 0.709930 0.42759 1.6603 19.5 0.112829562
## 2 Gender_bin 0.037910 0.04059 0.9341 32.6 0.357130094
## 3 Age 0.002079 0.00242 0.8594 161.9 0.391394595
## 4 Retired_bin 0.034894 0.03473 1.0048 324.9 0.315742725
## 5 Volunteer_rec -0.014677 0.02065 -0.7106 116.3 0.478738225
## 6 Lives_alone_bin -0.001329 0.04459 -0.0298 34.9 0.976388957
## 7 Phys_health_rating 0.023515 0.02516 0.9346 340.2 0.350672607
## 8 Multimorbidity_score 0.008094 0.00819 0.9880 49.6 0.327950608
## 9 Subj_vision_rating_aided 0.052368 0.02182 2.3998 338.3 0.016944619
## 10 Subj_hearing_rating_aided 0.014675 0.02873 0.5109 10.8 0.619704858
## 11 Subj_hearing_rating_unaided -0.223534 0.03132 -7.1376 17.6 0.000001378
## 12 Tinnitus_past_wk_bin 0.132370 0.03448 3.8385 107.2 0.000209721
## 13 SSQ15i_mean -0.006064 0.01343 -0.4516 194.2 0.652060424
## 14 SIM_mean 0.001875 0.00874 0.2145 41.4 0.831187153
## 15 Emocheq_mean -0.037440 0.02044 -1.8321 179.4 0.068600134
## 16 HHIES_total 0.006760 0.00304 2.2248 51.1 0.030536680
## 17 positive_SCI_bin 0.013761 0.05269 0.2612 369.1 0.794121095
## 18 CSRQ_mean -0.009462 0.05045 -0.1876 68.3 0.851772696
## 19 Mobility_needs_bin 0.101381 0.07892 1.2847 279.6 0.199968923
## 20 ABC_mean 0.001576 0.00157 1.0017 201.2 0.317707385
## 21 SWLS_mean -0.010625 0.01955 -0.5435 69.9 0.588530976
## 22 WHOQOL_overall_qol -0.000502 0.03967 -0.0127 28.9 0.989993706
## 23 WHOQOL_health_qol -0.034484 0.02168 -1.5908 274.3 0.112800880
## 24 WHO_money 0.022780 0.02134 1.0677 32.9 0.293405267
## 25 PHQ4_mean -0.049120 0.04548 -1.0799 35.3 0.287490776
## 26 Lonely_bin -0.067393 0.04781 -1.4097 66.6 0.163286183
## 27 Social_network_index 0.004471 0.01380 0.3241 118.0 0.746471961
## 28 Soc_part_freq -0.005070 0.02690 -0.1885 138.9 0.850774895
## 29 Soc_part_types -0.004853 0.01288 -0.3769 78.5 0.707240985
## 30 Motivate_mean -0.025452 0.01818 -1.3997 366.9 0.162450926
## 31 PTA4_better_ear 0.011353 0.00207 5.4901 59.1 0.000000889